Mondrian Conformal Regressors with Overlapping Categories

Henrik Boström, Ulf Johansson
Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, PMLR 329:279-293, 2026.

Abstract

Normalized conformal regressors have two potential limitations: i) they may generate prediction intervals that are several times larger than the largest observed absolute residual in the calibration set, and ii) the interval sizes may exhibit high dispersion even when using non-informative difficulty estimators. Mondrian conformal regressors provide a remedy by forming categories through equal-sized binning of the difficulty estimates and applying standard conformal regressors within each category. A drawback of this approach is that the mapping from difficulty estimates to prediction intervals may be very coarse, in particular for smaller calibration sets. Moreover, the calibration set size of each category cannot be fully controlled, potentially leading to overly conservative prediction intervals. We introduce a generalization of conformal predictors that allows overlapping Mondrian categories, and present an instantiation of this class for conformal regression. The proposed approach results in a smoother distribution of interval sizes while ensuring that each Mondrian category contains exactly the desired number of examples. A large-scale experimental evaluation on 33 datasets shows that the proposed approach consistently achieves superior average rankings with respect to prediction interval size compared with standard, normalized, and non-overlapping Mondrian conformal regressors over a range of difficulty estimators and significance levels.

Cite this Paper

BibTeX
@InProceedings{pmlr-v329-bostrom26a, title = {Mondrian Conformal Regressors with Overlapping Categories}, author = {Bostr{\"o}m, Henrik and Johansson, Ulf}, booktitle = {Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications}, pages = {279--293}, year = {2026}, editor = {Ahlberg, Ernst and Johansson, Ulf and Boström, Henrik and Carlevaro, Alberto and Hallberg Szabadváry, Johan and Carlsson, Lars}, volume = {329}, series = {Proceedings of Machine Learning Research}, month = {02--04 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v329/main/assets/bostrom26a/bostrom26a.pdf}, url = {https://proceedings.mlr.press/v329/bostrom26a.html}, abstract = {Normalized conformal regressors have two potential limitations: i) they may generate prediction intervals that are several times larger than the largest observed absolute residual in the calibration set, and ii) the interval sizes may exhibit high dispersion even when using non-informative difficulty estimators. Mondrian conformal regressors provide a remedy by forming categories through equal-sized binning of the difficulty estimates and applying standard conformal regressors within each category. A drawback of this approach is that the mapping from difficulty estimates to prediction intervals may be very coarse, in particular for smaller calibration sets. Moreover, the calibration set size of each category cannot be fully controlled, potentially leading to overly conservative prediction intervals. We introduce a generalization of conformal predictors that allows overlapping Mondrian categories, and present an instantiation of this class for conformal regression. The proposed approach results in a smoother distribution of interval sizes while ensuring that each Mondrian category contains exactly the desired number of examples. A large-scale experimental evaluation on 33 datasets shows that the proposed approach consistently achieves superior average rankings with respect to prediction interval size compared with standard, normalized, and non-overlapping Mondrian conformal regressors over a range of difficulty estimators and significance levels.} }
Endnote
%0 Conference Paper %T Mondrian Conformal Regressors with Overlapping Categories %A Henrik Boström %A Ulf Johansson %B Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications %C Proceedings of Machine Learning Research %D 2026 %E Ernst Ahlberg %E Ulf Johansson %E Henrik Boström %E Alberto Carlevaro %E Johan Hallberg Szabadváry %E Lars Carlsson %F pmlr-v329-bostrom26a %I PMLR %P 279--293 %U https://proceedings.mlr.press/v329/bostrom26a.html %V 329 %X Normalized conformal regressors have two potential limitations: i) they may generate prediction intervals that are several times larger than the largest observed absolute residual in the calibration set, and ii) the interval sizes may exhibit high dispersion even when using non-informative difficulty estimators. Mondrian conformal regressors provide a remedy by forming categories through equal-sized binning of the difficulty estimates and applying standard conformal regressors within each category. A drawback of this approach is that the mapping from difficulty estimates to prediction intervals may be very coarse, in particular for smaller calibration sets. Moreover, the calibration set size of each category cannot be fully controlled, potentially leading to overly conservative prediction intervals. We introduce a generalization of conformal predictors that allows overlapping Mondrian categories, and present an instantiation of this class for conformal regression. The proposed approach results in a smoother distribution of interval sizes while ensuring that each Mondrian category contains exactly the desired number of examples. A large-scale experimental evaluation on 33 datasets shows that the proposed approach consistently achieves superior average rankings with respect to prediction interval size compared with standard, normalized, and non-overlapping Mondrian conformal regressors over a range of difficulty estimators and significance levels.
APA
Boström, H. & Johansson, U.. (2026). Mondrian Conformal Regressors with Overlapping Categories. Proceedings of the Fifteenth Symposium on Conformal and Probabilistic Prediction with Applications, in Proceedings of Machine Learning Research 329:279-293 Available from https://proceedings.mlr.press/v329/bostrom26a.html.

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